Given the function y=-2(8x^(2)-9x-3)^(4), find (dy)/(dx) in any form. Answer: (dy)/(dx)=

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Given the function  y=-2(8x^(2)-9x-3)^(4), find  (dy)/(dx) in any form. Answer:  (dy)/(dx)=

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Identify function type and rule: Identify the type of function and the rule needed to differentiate it. The function y = -2(8x^2 - 9x - 3)^4 is a composite function, where an inner function (8x^2 - 9x - 3) is raised to a power and then multiplied by a constant. To differentiate this function, we will use the chain rule.Apply chain rule: Apply the chain rule. The chain rule states that the derivative of a composite function is the derivative of the outer function evaluated at the inner function times the derivative of the inner function. Let u = 8x^2 - 9x - 3, so y = -2u^4. The derivative of y with respect to u is dy/du = -2 * 4u^3 = -8u^3. Now we need to find du/dx.Find du/dx: Differentiate the inner function u = 8x^2 - 9x - 3 with respect to x. The derivative of u with respect to x is du/dx = 16x - 9.Substitute into chain rule: Substitute du/dx into the chain rule formula. We have dy/du = -8u^3 and du/dx = 16x - 9, so the derivative of y with respect to x is dy/dx = dy/du * du/dx = -8u^3 * (16x - 9).Replace u for final expression: Replace u with the original inner function to get the final expression for dy/dx. Substituting u back into the expression, we get dy/dx = -8(8x^2 - 9x - 3)^3 * (16x - 9).

Given the function $y=-2\left(8 x^{2}-9 x-3\right)^{4}$ , find $\frac{d y}{d x}$ in any form. $\newline$ Answer: $\frac{d y}{d x}=$

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Given the function y=−2(8x2−9x−3)4 y=-2\left(8 x^{2}-9 x-3\right)^{4} y=−2(8x2−9x−3)4, find dydx \frac{d y}{d x} dxdy​ in any form.\newlineAnswer: dydx= \frac{d y}{d x}= dxdy​=

Given the function $y=-2\left(8 x^{2}-9 x-3\right)^{4}$ , find $\frac{d y}{d x}$ in any form. $\newline$ Answer: $\frac{d y}{d x}=$